Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 36. C2×#13083549 | Q8 | semidirect |
| 38. #15667948 | Q8 | semidirect |
| 51. M32×C89 | Q8 | semidirect |
| 141. C89 | #13455 | semidirect |
| 172. M32 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030792 | 2 |
| C2×#19151423 | 2 |
| #26021035 | 2 |
| #26018361 | 2 |
| #26018347 | 2 |
| #26018342 | 2 |
| C89×#2159 | 2 |
| #13455 | 89 |